Assignment_1_solutions

Assignment_1_solutions - O O (1) (1) (7) (7) (9) (9) (6)...

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Unformatted text preview: O O (1) (1) (7) (7) (9) (9) (6) (6) O O (8) (8) O O O O O O O O O O (2) (2) O O O O O O (5) (5) O O (4) (4) (3) (3) Math 2860U -- Assignment 1 September 28, 2010 It's always useful to have a restart at the beginning of your maple session. restart; Problem 1: (supposed to be done by hand , but done in Maple here for fun, so you can see how to use Maple to solve problems step-by-step. Explanations on how you would do this by hand are provided.) Solve the separable ode: ode1 := diff(y(x),x)=8*x^2/(y+3); ode1 := d d x y x = 8 x 2 y C 3 with the initial conditions: x0 := 5; x0 := 5 y0 := -9; y0 := K 9 This equation is both separable and exact. Let's solve as separable. Separate the y to the left side, and the x to the right side, then integrate both sides accordingly. ls := integrate(y+3,y); ls := 1 2 y 2 C 3 y rs := integrate(8*x^2,x); rs := 8 3 x 3 Then the general solution is (don't forget that constant!) gensol:=ls=rs+C; gensol := 1 2 y 2 C 3 y = 8 3 x 3 C C Now to find C, we sub in the initial conditions...by hand, you replace x with 5 and y with -9 and solve for C. subs(x=x0,y=y0,gensol); 27 2 = 1000 3 C C and solve for C solve( (7) ,C); K 1919 6 ok, if doing this by hand, you'd get the solution below. exactsol := subs(C= (8) ,gensol); exactsol := 1 2 y 2 C 3 y = 8 3 x 3 K 1919 6 Since the solution is quadratic in y, there seem to be 2 possible solutions (10) (10) O O O O (14) (14) O O (12) (12) O O O O O O O O (13) (13) O O (18) (18) O O O O (15) (15) O O O O (19) (19) O O (11) (11) O O (17) (17) O O (16) (16) O O sols:={solve(exactsol,y)};...
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Assignment_1_solutions - O O (1) (1) (7) (7) (9) (9) (6)...

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